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Abstract

Advanced optical traps can probe single molecules with Ångstrom-scale precision, but drift limits the utility of these instruments. To achieve Å-scale stability, a differential measurement scheme between a pair of laser foci was introduced that substantially exceeds the inherent mechanical stability of various types of microscopes at room temperature. By using lock-in detection to measure both lasers with a single quadrant photodiode, we enhanced the differential stability of this optical reference frame and thereby stabilized an optical-trapping microscope to 0.2 Å laterally over 100 s based on the Allan deviation. In three dimensions, we achieved stabilities of 1 Å over 1,000 s and 1 nm over 15 h. This stability was complemented by high measurement bandwidth (100 kHz). Overall, our compact back-scattered detection enables an ultrastable measurement platform compatible with optical traps, atomic force microscopy, and optical microscopy, including super-resolution techniques.

Figures (7)

A wide variety of microscopy techniques can benefit from improved Ångstrom-scale precision and stability, including (a) a dual-beam optical-trap, (b) a surface-coupled optical trap, (c) atomic force microscopy, and (d) optical microscopy, particularly super-resolution techniques. In the first two assays, two focused lasers are used to measure opposite ends of a stretched molecule via scattered light. The ultimate limit to the precision of the position measurement is the differential-pointing stability between the lasers. This technique can be extended to actively stabilize the sample position for surface-coupled assays (b-d) using a reference mark attached to the sample.

Schematic of stabilization procedure using an out-of-loop monitor. Two modulated lasers scattered light from the same fiducial marker. The scattered light was detected on a common QPD, and the signals were electronically separated using lock-in amplifiers. After filtering and amplification, the signals were digitized by an FPGA, which used the signals to calculate the position of the sample. The 2.5-MHz signal stabilized the sample, while the 1-MHz signal provided an out-of-loop measurement. White boxes denote analog electronics. Grey boxes denote field programmable gate array (FPGA).

Simultaneous high-bandwidth detection of two lasers on a common detector. The normalized peak-to-peak voltage response of the detection system after demodulation is plotted as a function of the blinking rate of an LED placed immediately in front of the QPD.

Stabilization of an optical-trapping microscope to better than 1 nm in 3D over multiple hours. (a) Sample position versus time plotted during active stabilization as quantified by the out-of-loop detection laser [x (green), y (red), and z (blue)]. Data smoothed to 0.1 Hz for clarity. (b–d) Position-versus-time traces detail different 100-s time periods, emphasizing the Å-scale stability over any given 100-s period. Data smoothed to 10 Hz and offset vertically for clarity.

Sub-Å precision and stability over extended periods. The Allan deviation for the out-of-loop position record [Fig. 5(a)] plotted as function of averaging time for all 3 axes [x (green), y (red), and z (blue)]. The dashed line represents the expected improvement for averaging random noise.

Generation and detection of 1-Å steps. (a) Records of position versus time showing 1-Å steps detected with the out-of-loop laser (blue) as the stabilization set point of the in-loop signal (red) was updated by 1 Å every 2 s. (b) The Fourier transform of the pairwise distance difference between all pairs of points for both signals.